Mathematical modelling of signals recorded in noninvasive medical laser fluorescence diagnosis

Abstract

Based on the Kubelka-Munk two-flux model modified by the authors, which makes it possible in one-dimensional problems to obtain exact analytical expressions for radiation fluxes at the boundary of a turbid medium, and Kokhanovsky's solution for the radiation flux of fluorescence, questions are considered of modelling the spectrum of stimulated endogenous fluorescence of biological tissues as applied to problems of noninvasive medical diagnosis. An analytical expression is presented for the spectral distortion function, which depends on the scattering and absorption properties of cellular biological tissues and blood. It is shown that the model spectra agree well with the experimental data.

Nonlinear and nonmonotonic nature of the intensity of fluorescence emission on a surface of turbid fluorescing biotissues

“…It has to be special noted that in limits of our approach in the general case A f (λ e ) is not equal to the absorption coefficient μ af (λ e ) of the fluorophore (see explanations below). So in our previous paper there was a mistake in it 17 .…”

“…Unlike the Kokhanovsky's model in our approach there is no light incident on the left boundary of the medium at any fluorescence wavelength λ f as well. 16 all these statements can be written mathematically as the basic system of differential equations describing the forward I(x) and backward J(x) fluorescent fluxes as follows 17 :…”

“…16 showed the main source of errors in the classic KM model and proposed the generally improved version of the KM equations that makes it possible in one-dimensional (1D) problems to obtain exact values for radiation fluxes at boundaries of the medium (for the backscattered and transmitted fluxes detected by devices). This opens up prospects for constructing simple analytical and real-time algorithms to analyze easy the distortions of fluorescence spectra without resorting to complex multistep computations and numerical methods 17 . But in the above mentioned articles the problem of the linearity/nonlinearity of dependences of a registered fluorescence signal from the fluorophore concentration in tissues wasn't considered.…”

In vivo noninvasive measurement of skin autofluorescence biomarkers relate to cardiovascular disease in mice

“…SAF were used in the ultra-violet spectra through insertion of a spectral density filter for measurement of collagen, elastin, nicotinamide adenine dinucleotide (NADH), lipofuscin, pyridoxine, β-carotene and flavins. Wavelengths for the aforementioned biomarkers have previously been described using the LAKK-M system elsewhere (Smirnova et al, 2012;Rogatkin et al, 2013). The peak emission wavelengths used for the measurement of these compounds are as described in Table 1.…”